Did you know that the first written evidence of prime numbers was found in 1550 BC?

If a number cannot be divided into equal groups, then it is known as a prime number.

Can you divide 61 into equal groups of 2? Equal groups of 3 ? Groups of 4?

Let's find an answer to this question!

In this mini-lesson, we will explore the world of prime numbers by finding the answers to the questions like what is a prime number, is 61 a prime number, or if 61 is a composite number, etc., with the help of solved examples and interactive questions.

**Lesson Plan**

**What Is a Prime Number?**

A natural number that is greater than 1 which cannot be expressed as a product of any two other numbers is a prime number.

For example, 91 has just two factors: 1 and 91

So, 91 is a prime number.

**Is 61 a Prime Number?**

Let's determine the factors of 61 by prime factorization.

So, 61 can be expressed as \(61=1\times61\).

Clearly, it has only two factors.

So, 61 is a **prime number**.

**Is 61 a Composite Number? **

A composite number is a number that has more than two factors.

Moreover, if a number is not a prime number, then it is a composite number.

And vice versa is also true.

Therefore, 61 is **not** a** **composite number.

** **

- If any number has more than two factors, then it is not a prime number.
- 61 is a prime number.
- 1 is not a prime number.

**Solved Examples**

Example 1 |

In a class, the teacher told four students to pick random prime numbers.

Tiron, Paul, Yasmin, and Lebron have chosen 49, 61, 63, and 91 respectively.

Who do you think has chosen a prime number?

**Solution**

We have 4 numbers: 49, 61, 63, and 91.

The number 49 is divisible by 7. So, it is not a prime number.

The number 63 is divisible by 7 and 9. So, it is not a prime number.

The number 91 is divisible by 7. So, it is not a prime number.

So, the number chosen by Paul is a prime number. |

Example 2 |

Karen has to prove that 1 added or subtracted 61, makes it a composite number. How will she prove it?

**Solution**

On adding 1 to 61, Karen will get 62.

Factors of 62 =1, 2, 31, and 62.

Clearly, 62 has more than 2 factors. Thus, it is not a prime number.

On subtraction of 1 from 61, she will get 60.

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

It has factors other than 1 and 60, which makes it a composite number.

Hence 1 added or subtracted in 61, makes it a composite number.

\( \therefore \)1 added or subtracted in 61, makes it a composite number. |

- What are the twin prime numbers?

**Interactive Questions**

**Here are a few activities for you to practice. **

**Select/Type your answer and click the "Check Answer" button to see the result.**

**Let's Summarize**

The mini-lesson targeted the fascinating concept of knowing if 61 is a prime number or not. The math journey around the 61 being a prime number starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

**About Cuemath**

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.

**Frequently Asked Questions(FAQs)**

## 1. Why is 61 a prime number?

A natural number that is greater than 1 which cannot be expressed as a product of any two other numbers is a prime number.

Since 61 has just two factors: 1 and 61

Hence, 61 is a prime number.

## 2. What can 61 be divided by?

Divisors of 61 are the same as their factors i.e. 1, 3, 7, 9, 21, and 61.

## 3. Is 61 a prime number?

Yes, 61 is a prime number.